Question

a. suppose the multiplier is 1.5, the income multiplier with respect to the money supply is 2, the money multiplier is 4.5, and a central bank purchase of $6b of bonds during a recession drops the interest rate by one percentage point. suppose that to fight a recession, monetary policy is undertaken to lower the interest rate by two-thirds of a percentage point. what should happen to the income level?

b.suppose the short run Phillips curve is duch that a two-percentage point increase in inflation decreases unemployment by one percentage point. suppose the economy is in long run equilibrium with a real growth rate of 2% and an unemployment rate of 7% and the central bank increases the rate of growth of the money supply from 5% to 8%. when the economy has reached its new long run equilibrium, what will be the levels of inflation and unemployment?

c.suppose that in equilibrium the Canadian dollar is depreciating relative to the U.S. dollar by 5% per year. suppose changes in the U.S. cause the U.S. real interest rate to rise from 3.5% to 4.5% and the U.S inflation rate to increase from 4% to 6%. assuming a risk premium of one percentage point, after the canadian economy has settled to a new equilibrium, what is its nominal interest rate?

Answer 1

a).

Consider the given problem here the income multiplier with respect to money supply is “2”, => “dY/dM = 2”, => if money supply will increase $1billion, => the income will increase by “$2billion”. We have given that, if C.B. increases “M=money supply” by “$6billion”, then “the interest rate” drop by “1%” point. Now, suppose that to fight with the recession, monetary policy is undertaken to lower the “i” by “2/3” of a percent point, => here the C.B. have to increase money supply by, “2/3*6=$4billion”.

So, if money supply will increase by “$4billion”, => dY = 2*dM = 2*4 = $8billion.

b).

Here we have given that according to the SRPC “rate of inflation” will increase by “2%” if “unemployment rate” decreases by “1%”, => the slope of the PC is “dπ/du =(-2)”. Now, w have given that initially the output growth was “2%”, unemployment rate was “7%” and money supply growth rate was “5%”. So, here the inflation rate should be exactly equal to money supply growth. So, when C.B. increase the money supply growth from 5% to 8%, => the rate of inflation will also increase to 8%, => dπ = 8-5 = 3%, => du = dπ/(-2) = 3/(-2) = (-3/2) = (-1.5).

So, unemployment rate will decreases by (1.5%), => at the new LR equilibrium the unemployment rate will be “u=7-1.5=5.5%” and the inflation will be “π=8%”.

c).

Let’s assume that “Canada” be “home” and “USA” is foreign country here. So, according to the UIP(Uncovered Interest rate Parity) condition the “home” rate of return should be equal to the foreign rate of return plus the expected depreciation of home currency.

=> i(h) = i(f) + d, where d=depreciation of foreign currency.

According to the extended form of UIP there should be some “risk premium” in the foreign return, so now the following condition should hold, => i(h) = i(f) + d + rp, where rp=risk premium.

We have given that the new “real interest rate” is “4.5%” and the “inflation rate” is “6%” in USA, => i(f) = 4.5 + 6 =10.5%.

We also given that “Canadian” dollar depreciate by 5%, => d=5 and rp=1.

=> i(h) = i(f) + d + rp, => i(h) = 10.5 + 5 + 1 = 16.5, => i(h) = 16.5%.

So, at the new equilibrium the nominal interest rate is “16.5%”.